1. Steins;Gate. Alternates between hilarious comedy and OMGWTFISGOINGON OH MAN OH MAN mystery, while developing several intriguing characters and pushing along the single best plot I have ever seen. An incredible, intense, electrifying ride all the way through. If you like anime, watch this.
2. Naruto. Not enough people realize that Kishimoto created THE most intelligent fighting ever. No exaggeration, and not just in anime, but in any medium. Seriously, we have great debaters on this site arguing the matchups of various characters with excellent arguments on each side. Just try and debate who would win in a DBZ matchup, or a bleach matchup, or a fairy tail matchup. What is there to say? But on top of this, the fighting isn't just smart, it has turns and reveals that had me jumping off the edge of my seat and shouting, "OH, DAMN!! OH! OH!!!". Naruto+Sasuke vs Zabuza, Shikamaru vs. anyone, and Naruto vs. Pain are shining examples of what I'm talking about. The plot is exciting and unpredictable. Finally, Kishimoto created several fantastic characters that are a joy to watch, both on and outside the battlefield. Shikamaru, Itachi, Naruto, Kakashi, and Jiraiya come to mind.
2,5. Kakashi Gaiden. It's a part of Naruto really, but it deserves special mention. This is easily the best 45 minutes in Naruto. One, because it packed so much emotional power I cried the first four times I watched this. Next, because it showed what being a ninja is really all about. Naruto has it easy. All he has to do for the most part is beat the bad guy. Here's Kakashi, stealthily navigating enemy territory because every one of his opponents are a match for him or more, making life and death decisions for his subordinates -or are they his friends? If someone isn't sure whether or not Naruto can be brilliant, show them this. Again, this is the best of what Naruto has to offer.
3. Avatar: The Last Airbender. Ok I'm cheating, this is western animation with anime influences, not anime. But come on. The strength of this show comes in a few parts. The first is the incredible-looking fighting. The idea that you have to use martial arts movements to bend the elements was genius. The second, and most important part, is the characters. These are the the most engaging characters anywhere, with perhaps the sole exception of Harry Potters' titular character. The way they interact, develop, or when they are just being themselves, while watching you can't help but be glued to it all. It doesn't matter what they're doing. The third part is the comedy. Not much needs to be said other than I literally was laughing out loud, chuckling, or smiling during almost every episode. And the times I wasn't were because I wasn't supposed to. Finally, the whole series manages to capture a sense of grandness, or epic-ness. I can't describe it with one word. Some series are small, like many that are highschool drama based. This one is the opposite. The scope of what it deals with includes the identity of nations, of the world of men, of human nature and right and wrong. It's big stuff, know what I mean? In anycase, watch this. I couldn't stop until I was done, and I don't think most people reading this will be able to either. Seeing as there are three 24 episodes seasons, that's saying something.